Embedded Eigenvalues and the Nonlinear Schrodinger Equation

A common challenge to proving asymptotic stability of solitary waves is understanding the spectrum of the operator associated with the linearized flow. The existence of eigenvalues can inhibit the dispersive estimates key to proving stability. Following the work of Marzuola & Simpson, we prove the absence of embedded eigenvalues for a collection of nonlinear Schrodinger equations, including some one and three dimensional supercritical equations, and the three dimensional cubic-quintic equation. Our results also rule out nonzero eigenvalues within the spectral gap and, in 3D, endpoint resonances. The proof is computer assisted as it depends on the sign of certain inner products which do not readily admit analytic representations. Our source code is available for verification at http://www.math.toronto.edu/simpson/files/spec_prop_asad_simpson_code.zip.Comment: 29 pages, 27 figures: fixed a typo in an equation from the previous version, and added two equations to clarif

Building an IT Taxonomy with Co-occurrence Analysis, Hierarchical Clustering, and Multidimensional Scaling

Different information technologies (ITs) are related in complex ways. How can the relationships among a large number of ITs be described and analyzed in a representative, dynamic, and scalable way? In this study, we employed co-occurrence analysis to explore the relationships among 50 information technologies discussed in six magazines over ten years (1998-2007). Using hierarchical clustering and multidimensional scaling, we have found that the similarities of the technologies can be depicted in hierarchies and two-dimensional plots, and that similar technologies can be classified into meaningful categories. The results imply reasonable validity of our approach for understanding technology relationships and building an IT taxonomy. The methodology that we offer not only helps IT practitioners and researchers make sense of numerous technologies in the iField but also bridges two related but thus far largely separate research streams in iSchools - information management and IT management

Route Change Decision Making by Hurricane Evacuees Facing Congestion

Successful evacuations of metropolitan areas require overcoming unexpected congestion that reduces traffic flows. Congestion may result from accidents, incidents, or other events that reduce road capacity. Traffic professionals and emergency managers may promote deviations from planned routes to bypass an area of congestion and speed mass exit. However, some route changes may actually reduce traffic flow rates, and in these cases decision makers may want to discourage use of alternate routes. By using results of a behavioral survey of potential hurricane evacuees, this study identifies variables associated with the decision to alter routes and also identifies frequently used information sources. A dynamic traffic simulation with a decision-making model using this information is proposed as a means for evacuation decision makers to assess impacts of driver decisions. Results from more than 800 responses showed the potentially strong influence of effective advanced traveler information systems to support decisions made by hurricane evacuees on whether to use an alternate route when faced with congestion. Results of this study are a timely contribution to those seeking a better understanding of driver behavior during evacuations and improvement of emergency management efficiency and efficacy

Selection of Source and Use of Traffic Information in Emergency Situations

The access and the use of advanced traveler information systems (ATISs) by drivers during normal commuting have been extensively assessed and analyzed. Emergency managers and transportation officials have extended the results of studies of ATIS use under routine conditions to emergency scenarios under the assumption that drivers\u27 responses to information under emergency conditions mimic those seen under normal driving conditions. A recent survey of potential hurricane evacuees suggests the need to revisit this assumption. Results indicate that although commercial radio reports and variable message signs continue to be the sources of traffic information cited the most frequently, other information sources (mobile phones, in-car systems such as Global Positioning System devices, and the Internet) have significantly increased in importance. Rapid growth in user rates and the relatively low cost of implementation suggest that a revision of plans for emergency transportation information communications may be warranted. Better, more effective use of ATISs during emergency situations, especially when traffic incidents occur, may lead to improved and more reliable travel times and improved safety and emergency response. With the use of factor analysis, four driver personalities are identified, with each one characterized by the proclivity for and response to traffic information. This information will be of interest to developers and users of ATISs and to those responsible for emergency management and transportation planning

Evacuee Route Choice Decisions in a Dynamic Hurricane Evacuation Context

Very high traffic volumes may lead to extensive congestion during hurricane evacuations. Evacuation planners reduce this congestion by careful planning for multiple hurricane scenarios and assignment of evacuation routes and timing. This planning may be for naught if obstructions block key roadways. An advanced traveler information system (ATIS) may be used to guide evacuees to alternate routes, but how effective will that guidance be? Should the use of alternate routes be encouraged? How are drivers likely to respond to delays and information? Will information shorten or improve the reliability of travel times in emergency conditions? Integration of a dynamic evacuation simulation and a decision-making model (representative of the decisions made by potential hurricane evacuees when provided with information on downstream traffic congestion and alternate routes) can help emergency planners prepare for the unexpected. Advance modeling of likely accident locations and the severity can forecast the effects of alternate route use, help determine the best locations and timing of alternate route information, and support decision making. This study integrated an evacuee route choice decision model and a mesoscopic evacuation transportation simulation for southeastern Virginia. Study results show how the effects of ATIS can be tested in advance, thus allowing more comprehensive planning by emergency management and transportation professionals. Simulations of ATIS\u27 effectiveness in evacuation scenarios have been largely unexplored. Methods presented can be applied in a variety of evacuation scenarios and may be of particular value to emergency planners